What is the molality of a 15.0 M solution of phosphoric acid with a density of 1.65 g/mL?

May 31, 2018

The molal concentration is 83.3 mol/kg.

Explanation:

Assume that you have one litre of the phosphoric acid solution.

Step 1. Calculate the mass of the solution

$\text{Mass of solution" = 1000 color(red)(cancel(color(black)("mL solution"))) × "1.65 g solution"/(1 color(red)(cancel(color(black)("mL solution")))) = "1650 g solution}$

Step 2. Calculate the mass of ${\text{H"_3"PO}}_{4}$

${\text{Mass of H"_3"PO"_4 = 15.0 color(red)(cancel(color(black)("mol H"_3"PO"_4))) × ("98.00 g H"_3"PO"_4)/(1 color(red)(cancel(color(black)("mol H"_3"PO"_4)))) = "1470 g H"_3"PO}}_{4}$

Step 3. Calculate the mass of water

$\text{Mass of water = 1650 g - 1470 g = 180 g}$

So, the solution contains ${\text{15.0 mol H"_3"PO}}_{4}$ and 180 g water.

Step 4. Calculate the moles of ${\text{H"_3"PO}}_{4}$ in 1 kg water

${\text{Moles of H"_3"PO"_4 = 1000 color(red)(cancel(color(black)("g water"))) × ("15.0 mol H"_3"PO"_4)/(180 color(red)(cancel(color(black)("g water")))) = "83.3 mol H"_3"PO}}_{4}$

∴ The molal concentration is 83.3 mol/kg.